additional mathematics paper 1

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SULIT 3472/1 NO.KAD PENGENALAN/I.C NUMBER - - ANGKA GILIRAN/INDEX NUMBER LOGO SEKOLAH _________________________________ PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2007 ADDITIONAL MATHEMATICS Paper 1 2 hours JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Tuliskan angka giliran dan nombor kad pengenalan anda pada ruang yang disediakan. Write your index number and I.C. number in the space provided. 2. Calon dikehendaki membaca arahan di halaman 2 dan halaman 3 Candidates are required to read the intructions on page 2 and 3 3472/1 SULIT Examiner’s Question Full Marks obatine Marks Acquire 1 2 2 4 3 3 4 3 5 4 6 3 7 4 8 4 9 3 10 3 11 2 12 4 13 3 14 3 15 3 16 4 17 3 18 2 19 3 20 3 21 4 22 3 23 4 24 3 25 3 Total 80 3472/1 Form Five Additional Mathematics Paper 1 September 2007 Nama Calon : Tingkatan :

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Page 1: Additional Mathematics Paper 1

SULIT 3472/1

NO.KAD PENGENALAN/I.C NUMBER- -

ANGKA GILIRAN/INDEX NUMBER

LOGO SEKOLAH_________________________________

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2007

ADDITIONAL MATHEMATICSPaper 12 hours

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor kad pengenalan anda pada ruang yang disediakan.

Write your index number and I.C. number in the space provided.

2. Calon dikehendaki membaca arahan di halaman 2 dan halaman 3

Candidates are required to read the intructions on page 2 and 3

____________________________________________________________________________________________________________________________________________________

Kertas soalan ini mengandungi 20 halaman bercetak.

3472/1 SULIT

Examiner’s CodeQuestion Full Marks

Marks Acquired1 22 43 34 35 46 37 48 49 310 311 212 413 314 315 316 417 318 219 320 321 422 323 424 325 3

Total 80

3472/1Form FiveAdditional MathematicsPaper 1September 20072 hours Nama Calon :

Tingkatan :

Page 2: Additional Mathematics Paper 1

SULIT 3472/1

MAKLUMAT UNTUK CALON

1. Kertas soalan ini mengandungi 25 soalan.

2. Jawab semua soalan.

3. Bagi setiap soalan berikan SATU jawapan sahaja.

4. Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas

soalan.

5. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu

anda untuk mendapatkan markah.

6. Sekiranya anda hendak menukarkan jawapan, batalkan kerja mengira yang telah

dibuat. Kemudian tuliskan jawapan yang baru.

7. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.

8. Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan

dalam kurungan.

9. Satu senarai rumus disediakan di halaman 4 hingga 6.

10. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

11. Kertas soalan ini hendaklah diserahkan di akhir peperiksaan.

3472/1 SULIT

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Page 3: Additional Mathematics Paper 1

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INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

2. Answer ALL questions.

3. Give only ONE answer for each question.

4. Write your answer clearly in the spaces provided in the question paper.

5. Show your working. It may help you to get marks.

6. If you wish to change your answer, cross out the work that you have done. Then write

down the new answer.

7. The diagram in the questions provided are not drawn to scale unless stated.

8. The marks allocated for each question and sub-part of a question are shown in

brackets.

9. A list of formulae is provided on pages 4 to 6.

10. You may use a non-programmable scientific calculator.

11. This question paper must be handed in at the end of the examination.

[See overleaf3472/1 SULIT

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Page 4: Additional Mathematics Paper 1

SULIT 3472/1

ALGEBRA

1 8

2 am x an = a m + n 9 Tn = a + (n -1)d

3 am an = a m – n 10 Sn =

4 ( am )n = a m n 11 Tn =

5 12

6 13

7 log a mn = n log a m

CALCULUS

1

4 Area under a curve=

2

3 5 Volume generated

= or

=

STATISTICS

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Page 5: Additional Mathematics Paper 1

SULIT 3472/1

1 8

2 9

3 10

4 11 P(X = r) =

5 12 Mean =

6 13

7 14

GEOMETRY

1 Distance =

4 Area of a triangle =

2 Midpoint = 5.

3 A point dividing a segment of a line

(x , y ) = 6

[See overleaf3472/1 SULIT

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Page 6: Additional Mathematics Paper 1

SULIT 3472/1

TRIGONOMETRY

1 Arc length, s =r8

2 Area of a sector, 9

3 . 10

4 11

5 12

6 sin 2A = 2 sin A cos A 13

7 cos 2A = = =

14 Area of triangle =

Answer all questions.

3472/1 SULIT

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M ={ -3, -2, -1, 0, 1, 2 }

N ={ -1, 0, 1, 2, 3 }

Page 7: Additional Mathematics Paper 1

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1 Based on the above information, the relation between M and N is defined by the set

of ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}. State

(a) the image of 2. (b) the object of 0.

[2 marks]

Answer : (a)…………………………………

(b)…………………………………

2 Given that f : x 3x – 4 and g : x x 2 +8 x + 16, find

(a) f -1 ( 5 )(b) g f ( x )

[4 marks]

Answer : (a)…………………………………

(b)…………………………………

3 -3 is one of the roots of the quadratic equation 2 x2 + p x =3 Find

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2

1

4

2

Page 8: Additional Mathematics Paper 1

SULIT 3472/1

( a ) the value of p ( b ) the value of the other root.

[3 marks]

Answer : (a)…………………………………

(b)…………………………………

4. The quadratic equation ( 2 x – 5 )2 = (p – 10) x has two distinct roots.

Find the range of values of p.

[3 marks]

Answer : …………………………………

5. Solve

[4 marks]

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3

3

3

4

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Answer : …………………………………

6. Solve the equation .

[3 marks]

Answer : …………………………………

7. During the year 2005, a company increased its sales of digital cameras at a constant rate of 200 units per month. Thus the number of digital cameras sold in February

[See overleaf3472/1 SULIT

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4

5

3

6

Page 10: Additional Mathematics Paper 1

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was 200 more than in January, the number of digital cameras sold in March was 200 more than in February, and this pattern continued month by month throughout the year. Given that the company sold 38,400 units of digital cameras in the year 2005.

Calculate the number of units of digital cameras sold in

(a) January 2005 (b) December 2005

[4 marks]

Answer : (a)…………………………………

(b)…………………………………

8. The first three terms of a geometric progression are x+10, x-2 and x-10 respectively. Calculate

(a) the value of x.

(b) the sum to infinity of this progression.[4 marks]

Answer : (a)…………………………………

(b)…………………………………

9. A point P (8, t ) divides the line joining A (4, 1) and B ( r , 7 ) such that 3AP = 2PB. Find the value of

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4

7

4

8

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(a) r

(b) t[3 marks]

Answer : (a)…………………………………

(b)…………………………………

10. The straight lines y = mx + 9, where m is a constant, and 2y = x 2 are

perpendicular.

(a) Find the value of m,

(b) Hence or otherwise, find the coordinates of the point of intersection of the lines.

[3 marks]

Answer : (a)…………………………………(b)…………………………………

11 Diagram 1 shows vectors and . A, B and C are ( 0, h ), ( 5, 3 ) and ( 2, 7 ) respectively.

[See overleaf3472/1 SULIT

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3

9

3

10

Page 12: Additional Mathematics Paper 1

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DIAGRAM 1

(a) Express in the form of

(b) Given that , find the corresponding value of h.

[2 marks]

Answer : (a)…………………………………

(b)… ………………………………

12 Diagram 2 shows a parallelogram ABCD with BED as a straight line.

3472/1 SULIT

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A

B

C

D

E

DIAGRAM 2

2

11

O

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Given that p, = 3q, and 4DE = EB. Express in terms of p and q :

(a)

(b)

[4 marks]

Answer : (a)…………………………………

(b)… ………………………………

13. Given that , and . Find

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4

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Page 14: Additional Mathematics Paper 1

SULIT 3472/1

(a)

(b) unit vector in the direction of .[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

14. The net value, m in hundreds of ringgit, of the monthly output of a factory is

modelled by where n is the number of working hours a worker put

in per month. Calculate the value of n such that m is maximum.[3 marks]

Answer : n =…………………………………

15 The radius of a spherical balloon is increasing at the rate of x cms-1. Given that the rate of change of the volume of the balloon is 25 cm3 s -1 when

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3

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3

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Page 15: Additional Mathematics Paper 1

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its radius is 5 cm. Find the value of x. [ ]

[3 marks]

Answer : …………………………………

16 x and y are related by the equation , where m and n are constants.

A straight line is obtained by plotting xy against x2, as shown in Diagram 3.

Calculate the value of m and of n.[4 marks]

Answer : m=…………………………………

n=…………………………………

17 Given that , find the value of m if

[See overleaf3472/1 SULIT

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xy

(12, 2 )

( 6, 0) x 2

DIAGRAM 3

4

16

3

15

Page 16: Additional Mathematics Paper 1

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[3 marks]

Answer : …………………………………

18 Diagram 4 shows the quadratic curve y = g(x) and the line PQ. PQ is parallel to the x-axis.

Given that the curve has a minimum value at O, the origin, the curve

intersects line PQ at R (b, 4). Given that the area of the shaded region is .

Find

[2 marks]

Answer : …………………………………

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2

18

3

17

P Q

O

y

x

y = g(x)

DIAGRAM 4

R(b,4)

Page 17: Additional Mathematics Paper 1

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19 A circle of radius 2.5 cm has a minor sector with an area of 6.25 cm2. Calculate

( a ) the angle of the sector in radians,

( b ) the perimeter of the major sector.

[ use ][3 marks]

Answer : (a)…………………………………

(b)… ………………………………

20 Given that x is an acute angle and , find 1+ in terms of

m and n.[3 marks]

Answer : …………………………………

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3

20

3

19

Page 18: Additional Mathematics Paper 1

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21 Solve 3cos 2x + 4 cos x +1 = 0 for [4 marks]

Answer : …………………………………

22 An expedition team consisting of 10 members to be chosen from a group of 4 teachers and 12 students.

(a) Calculate the number of teams that can be formed.

(b) If the team must consist of at least 2 teachers, calculate the numbers of teams that could be formed.

[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

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4

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Page 19: Additional Mathematics Paper 1

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23 (a) How many possible arrangements in a row, can all the letters from the word “ C E R I A “ be arranged ?

(b) An arrangement in (a) is chosen at random, find the probability that the arrangement will have both ‘A’ and ‘E ‘ separated.

[4 marks]

Answer : (a)…………………………………

(b)… ………………………………

24 Diagram 5 shows a standard normal distribution graph.

The probability represented by the area of the shaded region is 0.803.

(a) Find the value of P( Z > k )

(b) X is a continuous random variable which is normally distributed with a mean of and a standard deviation of 2. If the value of X is 85 when the Z-score is k,

find the value of .[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

[See overleaf3472/1 SULIT

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-k k z

f(z))

0.803

DIAGRAM 5

3

24

4

23

Page 20: Additional Mathematics Paper 1

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25 In a survey, the probability that a family owning one unit of computer is 0.6. N families were selected at random. The standard deviation of the numbers of family owning one unit of computer is 1.697.

Find(a) the value of N(b) the mean of the numbers of family owning one unit of computer.

[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

END OF QUESTION PAPER

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